How to plot the least square method?

Hello!

I have these measurements of an experiment where Kp and Kd are the coefficients of PD controller and model displays critical damping at these measurements.

I want to find the ideal curve with respect to least sqruare method.

How to do that?

I tried that but I don't know if is true.

plot(Kd,Kp,'go')
hold on
f = fit(Kd,Kp,'poly2');
plot(f,Kd,Kp,'b--')
xlim([0.2,1.3])
ylim([-2,22])
legend('Location','NorthWest');
hold off

[Star Strider]

Kd_Kp = readtable('https://www.mathworks.com/matlabcentral/answers/uploaded_files/595780/Kd_Kp.xlsx')

Kd_Kp = 4×2 table
    Kp    Kd 
    __    ___

     1    0.3
     5    0.6
    10    0.8
    20    1.2

figure
scatter(Kd_Kp.Kd, Kd_Kp.Kp, 'filled')
xlabel('K_d')
ylabel('K_p')
grid

Since there are so few points, your options are limited!

[RoBoTBoY]

How do I connect these points with a curve?

So this diagram I drew is wrong?

[Star Strider]

'How do I connect these points with a curve?’

Whatever works, unless you have a mathematical model of the process that created them, and in that instance, use that mathematical model with a linear or nonlinear parameter estimation function. Then, using that function and the estimated parameters, calculate the fit and plot the line using those data.

One option is a spline fit —

Kd_Kp = readtable('https://www.mathworks.com/matlabcentral/answers/uploaded_files/595780/Kd_Kp.xlsx')

Kd_Kp = 4×2 table
    Kp    Kd 
    __    ___

     1    0.3
     5    0.6
    10    0.8
    20    1.2

Kd_v = linspace(min(Kd_Kp.Kd), max(Kd_Kp.Kd));
Kp_v = spline(Kd_Kp.Kd, Kd_Kp.Kp, Kd_v);
    
figure
scatter(Kd_Kp.Kd, Kd_Kp.Kp, 'filled')
hold on
plot(Kd_v, Kp_v, '-r')
hold off
xlabel('K_d')
ylabel('K_p')
grid
legend('Data','Spline Fit', 'Location','best')

It all depends on the result you want, and the process that created the data.